The victim, identified as Babita, fell into the borewell in Mitramandal colony while she was playing with other children, they said.
A rescue operation was launched by the local authorities with the help of State Disaster Response Team (SDRF) and another hole was dug parallel to the borewell.
The girl, who was inside the borewell with almost no oxygen, was taken out by the rescue team after around four hours, police said.
She was rushed to the Patna Medical College and Hospital (PMCH) and admitted in the Intensive Care Unit (ICU) but died during treatment, they said.
